A horizontal circular platform rotates counterclockwise about its axis at the ra

Question

A horizontal circular platform rotates counterclockwise about its axis at the rate of 0.971 rad/s. You, with a mass of 66.5 kg, walk clockwise around the platform along its edge at the speed of 1.19 m/s with respect to the platform. Your 20.3-kg poodle also walks clockwise around the platform, but along a circle at half the platform's radius and at half your linear speed with respect to the platform. Your 18.7-kg mutt, on the other hand, sits still on the platform at a position that is 3/4 of the platform's radius from the center. Model the platform as a uniform disk with mass 90.1 kg and radius 1.97 m. Calculate the total angular momentum of the system.

Explanation / Answer

Given

Circular platform rotates ccw 90.1 kg, radius 1.97 m, 0.971 rad/s
You 66.5 kg, cw 1.19 m/s, at r
Poodle 20.3 kg, cw 1.19/2 m/s, at r/2
Mutt 18.7 kg, 3r/4

You

Relative
= v/r
= 1.19/1.97
= 0.6040
Actual
= 0.971 - 0.6040
= 0.367

I = mr^2
= 66.5*1.97^2
= 258.07
L = I
= 258.07*0.367
= 94.71

Poodle

Relative
= (1.19/2)/(1.97/2)
= 0.586
Actual
= 0.971 - 0.586
= 0.385

I = m(r/2)^2
= 20.3*(1.97/2)^2
= 19.69
L = I
= 19.69*0.385
= 7.58

Mutt

Actual
= 0.971
I = m(3r/4)^2
= 18.7(3*1.97/4)^2
= 40.82
L = I
= 40.82*0.971
= 39.63

Disk

I = mr^2/2
= 90.1(1.97)^2/2
= 174.83
L = I
= 174.83*0.971
= 169.76

Total
L = 94.71 + 7.58 + 39.63 + 169.76
= 311.68 kg m^2/s

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